Blowup of solutions for the “bad” Boussinesq-type equation ✩

The paper studies the blowup of solutions to the initial boundary value problem for the “bad” Boussinesq-type equation ut t −uxx −buxxxx = σ(u)xx, where b >0 is a real number and σ(s) is a given nonlinear function. By virtue of the energy method and the Fourier transform method, respectively, it proves that under certain assumptions on σ(s) and initial data, the generalized solutions of the above-mentioned problem blow up in finite time. And a few examples are shown, especially for the “bad” Boussinesq equation, two examples of blowup of solutions are obtained numerically.  2003 Elsevier Inc. All rights reserved